Question

By a theorem of Landau, a nonnegativity condition ensures that these objects exhibit a singularity. A modified operation on arithmetic functions is computed as the inverse Mellin transform of one of these objects in Perron’s formula, which can be used to prove Harald Bohr’s theorem on abscissae of convergence. One of these objects named for Hasse and Weil is associated to an elliptic curve in the analytic statement of the (-5[1])Birch and Swinnerton-Dyer conjecture. (-5[1])Two of these objects may be multiplied using their namesake’s form of (*) convolution. When the coefficients of these objects are generated by a character, they are called L-functions and can be used to prove (-5[1])that there are infinitely many primes in arithmetic progressions. For 10 points, (-5[1])the Riemann zeta function (-5[1])is an example of what infinite (-5[2])sums (-5[1])of the form “a-sub-n (-5[2])times (-5[1])n to the negative s,” named for the French-German formulator of the pigeonhole (0[1])principle? (10[2])■END■ (10[4]0[4])

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